One Classification Of Theta Curves Up To Eight Crossings

The classification of prime spatial curves by crossing numbers under topological meaning is the crucial contents in studying spatial graph which is similar to the kont theory.Since the complete classification of all prime Theta curves up to seven crossings is well known.In this paper we try to constuct one Theta curve with eight crossings by adding two vertices and one simple arc which would not cause the extra crossings to the least crossing number projective diagram of eight-crossing prime kont,and prove it to be a prime Theta curve with eight crossings. More specifically, we take one prime kont81for example,get all prime Theta curves(the set is (?)(8,)) on its least crossing number projective diagram and classify these theta curves up to ambient isotopy using Yamada polynomial.At last,we classify and enumerate all prime Theta curves up to seven crossings using this method of adding edges,the result is the same with Litherland’table.The main result:(?)(8,) contains six prime theta curves at least with eight crossings up to ambient isotopy.